Algebra Examples

$\frac{6}{- 3 - \sqrt{13}}$

Step 1

Multiply $\frac{6}{- 3 - \sqrt{13}}$ by $\frac{- 3 + \sqrt{13}}{- 3 + \sqrt{13}}$ .

$\frac{6}{- 3 - \sqrt{13}} \cdot \frac{- 3 + \sqrt{13}}{- 3 + \sqrt{13}}$

Step 2

Multiply $\frac{6}{- 3 - \sqrt{13}}$ by $\frac{- 3 + \sqrt{13}}{- 3 + \sqrt{13}}$ .

$\frac{6 (- 3 + \sqrt{13})}{(- 3 - \sqrt{13}) (- 3 + \sqrt{13})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{6 (- 3 + \sqrt{13})}{9 - 3 \sqrt{13} + 3 \sqrt{13} - {\sqrt{13}}^{2}}$

Step 4

Simplify.

$\frac{6 (- 3 + \sqrt{13})}{- 4}$

Step 5

Cancel the common factor of $6$ and $- 4$ .

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Step 5.1

Factor $2$ out of $6 (- 3 + \sqrt{13})$ .

$\frac{2 (3 (- 3 + \sqrt{13}))}{- 4}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $- 4$ .

$\frac{2 (3 (- 3 + \sqrt{13}))}{2 (- 2)}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (3 (- 3 + \sqrt{13}))}{2 \cdot - 2}$

Step 5.2.3

Rewrite the expression.

$\frac{3 (- 3 + \sqrt{13})}{- 2}$

Step 6

Move the negative in front of the fraction.

$- \frac{3 (- 3 + \sqrt{13})}{2}$

Step 7

Rewrite $- 3$ as $- 1 (3)$ .

$- \frac{3 (- 1 (3) + \sqrt{13})}{2}$

Step 8

Factor $- 1$ out of $\sqrt{13}$ .

$- \frac{3 (- 1 (3) - 1 (- \sqrt{13}))}{2}$

Step 9

Factor $- 1$ out of $- 1 (3) - 1 (- \sqrt{13})$ .

$- \frac{3 (- 1 (3 - \sqrt{13}))}{2}$

Step 10

Simplify the expression.

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Step 10.1

Move the negative in front of the fraction.

$- - \frac{3 (3 - \sqrt{13})}{2}$

Step 10.2

Multiply $- 1$ by $- 1$ .

$1 \frac{3 (3 - \sqrt{13})}{2}$

Step 10.3

Multiply $\frac{3 (3 - \sqrt{13})}{2}$ by $1$ .

$\frac{3 (3 - \sqrt{13})}{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (3 - \sqrt{13})}{2}$

Decimal Form:

$- 0.90832691 \dots$